Liu Yi^{1, 2} Sun Dayuan^{1} Yu Yuhe^{2} Qu Songsheng^{1} Shen Yunfen^{2}
(^{1}Department of Chemistry, College of Chemistry and Molecular Sciences, Wuhan University, Wuhan 430072, China; ^{2}Laboratry of Protozoology, Institute of Hydrobiology, Chinese Academy of Science, Wuhan 430072, China)
Received Sep.6, 2001; Supported by the National Natural Science Foundation of China (NSFC), and Young Mainstay Teachers’ Program of Chinese Educational Ministry.
Abstract The heat output of the growth metabolism of Tetrahymena pyriformis has been determined by using a LKB2277 BioActivity Monitor at 25°C. From the thermogenic curves, it can be established that thermokinetic equation of their growth metabolism is P_{t} = P_{t=0} exp(k_{m} t), dP / dt = k_{m} P^{1} ,with the order of growth metabolism n = 1. The experimental results indicate that the relationship between the metabolic power (P) and the cell concentration (C), and relationship between the metabolic power of each cell (P_{0}) and the cell concentration (C) can be characterized by the following thermal equations: P = A + K C, P_{0} = A’ + K’ ln C or dC / dP_{0} = C^{1} .The order of the P_{0}–C equation is also 1. These results are very significant in environmental sciences, biology and thermochemistry.
Keyword Tetrahymena pyriformis, growth metabolism, microcalorimetry, thermokinetics, thermal chemical equations.

INTRODUCTION
In recent years, biological calorimetry is attracting increasing attention^{[1]}. Microcalorimetry has demonstrated its power as a universal, integral, nondestructive and highly sensitive tool for many environmental questions, it can provide a lot of kinetic and thermodynamic information. Several monographs and some articles offer comprehensive discussion on environmental and biological applications^{[19]}. Nevertheless, microcalorimetry can still provide some unexpected surprises and unwanted pitfalls, they are very significant for study of cell metabolic processes.
Microcalorimetry is very useful for fundamental studies of growth metabolism of cells. Thus the metabolic process of living cells can be studied through monitoring the heat effects with sufficiently sensitive calorimeters^{[10]}. In general, the metabolism of cells is very complicated. In the present work, a LKB2277 BioActivity monitor has been used to determine the heat output of the growth metabolism ofTetrahymena pyriformis.
Tetrahymena pyriformis belongs to the protoza family and is widely distributed, it is an important kind of environmental microorganism. It can be collected from polluted water, and can be separately cultured into a bacteriafree species because it is easily cultured and preserved in the laboratory. Tetrahymena pyriformis is an eukaryotic monocellular animal. It can be used as a biological indicator in freshwater biology and environment pollution studies. At the same time, it has been used widely as a “test animal” to monitor and evaluate toxicants, nutrients, antibiotics, anticancer medicaments etc.^{[11]}. 
MATERIAL AND METHODS
2.1 Instrument
A LKB2277 BioActivity Monitor was used to determine the metabolic powertime curves ofTetrahymena pyriformiscells. The performance of this instrument and the details of its construction have been previously described^{[1214]}.
2.2 Materials
Tetrahymena pyriformis (BJ4, mononuclear) was provided by the Department of Biology, Beijing University.
The culture medium was a solution containing the nutrients peptone 1 wt. %, beef extract 0.1 wt. % and glucose 0.5 wt. %.
2.3 Cleaning procedure for the flowcell
The flowcell was cleaned and sterilized as follows: (1) sterilized distilled water was pumped through the system for 30min at a flow rate of 40ml·h^{1}; (2) a 0.1mol/L solution of HCl was pumped through the system for 30min at a flow rate of 40ml·h^{1}; (3) a 75% alcohol solution was pumped through the system for 30min at a flow rate of 25ml·h^{1}; (4) a solution of 0.1mol / L NaOH was pumped through the system for 30min at a flow rate of 40ml·h^{1}; (5) sterilized distilled water was again pumped through the system for 30min at a flow rate of 40ml·h^{1}.
2.4 Microcalorimetric determination
Once the system was cleaned and sterilized, sterilized distilled water was pumped through the system at a flow rate of 10ml / h to run the baseline. After a stable baseline had been obtained, the bacteriafree Tetrahymena pyriformis species, which had been cultured pure, was added to 80 ml of liquid medium, and cultured at 25°C by the cycleflow method. A schematic representation of the experimental apparatus has been shown in Fig.1. The preparation was monitored and its thermogenic curves were obtained.
When the pen of the chart recorder starts rising, this indicates that the Tetrahymena pyriformis cells are entering an exponential growth state. A sample (3.0 ml) was removed at this stage, 1 ml of 1% formaldehyde solution was added to kill the organism, and the population density was measured with a haemocytometer.
Fig.1 A schematic representation of the experimental apparatus

RESULT AND DISCUSSION
3.1 Growth thermogenic curve of Tetrahymena pyriformis at25°C
The metabolic processes of Tetrahymena pyriformis in culture media was studied and the growth thermogenic curve recorded. A typical experimental curve is shown in Figure 2, there is a turning point ( B ) in the metabolic thermogenic curve, it consists of two parts, a log phase (AB) and a decline phase (BC). They are two very interesting and characteristic phase of growth metabolism.Fig.2 Growth thermogenic curve of Tetrahymena pyriformis at 25°C
3.2 Thermokinetic equation
In the log phase of growth (AB), the cell is growing exponentially. If the cell number is n_{0} at time 0, and n_{t} at time t, then
n_{t} = n_{0} exp(k t) (1)
k is the growth rate constant. If the power output of each cell is w, then
n_{t} w = n_{0} w exp(k t) (2)
P_{t=0} = n_{0} w and P_{t} = n_{t} w, giving
P_{t} = P_{t=0} exp(k t)
or ln P_{t} = ln P_{t=0} + k t (3)
The thermogenic curves of the log phase of growth correspond to Eq.(3). So, making use of the data P_{t} and t taken from the curve (shown as AB part) to fit a linear equation, one can obtain the growth rate constant k. The rate constant k of Tetrahymena pyriformis growth was shown in Table 1.
Table 1 Rate constants for Tetrahymena pyriformis growth at 28°C
Experiment No.  1  2  3  4  5  6  mean value 
k (min^{1})  0.0137  0.0119  0.0122  0.0127  0.0134  0.0132  0.0128±0.0006 
R  0.9958  0.9965  0.9965  0.9980  0.9997  0.9976  0.9974 
From the data in Table 1, it is apparent that all of the correlation coefficients, R, are greater than 0.9950, indicating a good reproducibility and correlationship.
Data in Table 1 clearly indicate that the relationship between lnP and metabolic time t satisfies a linear equation, i.e, for log phase,
ln P = ln P _{t=0} + k_{m} t .
Eq. (3) can be rewritten as
dP /dt = k P = k P^{n} , n = 1 (4)
Eq. (4) is the thermokinetic equation of Tetrahymena pyriformis growth metabolism, with the order of growth n=1.
3.3 Data for the growth metabolism
The corresponding P (mW) and C (cells·ml^{1}) vs. t data of the log phase (AB) are given in Table 2, and the corresponding P (mW) and C (cells.ml^{1}) data of the decline phase (BC) are given in Table 3.
Table 2 P_t and C–t data for growth metabolism of Tetrahymena pyriformis ( log phase, 25°C)
P mW 
ln P 
C cells per 0.6 ml 
ln C 
P_{0} nW per cell 
13.7 18.6 30.2 51.9 91.6 121.7 172.8 
2.617 2.923 3.407 3.949 4.517 4.802 5.152 
14700 16300 19500 23200 27800 33000 39300 
9.595 9.699 9.878 10.052 10.233 10.404 10.579 
0.93 1.14 1.55 2.24 3.29 3.69 4.40 
* Volume of the measuring cell is 0.6ml.
Table 3 P_t and C–t data for growth metabolism of Tetrahymena pyriformis ( decline phase, 25°C)
P mW 
ln P  C cells per 0.6 ml 
ln C  P_{0 }nW per cell 
146.2 122.3 91.8 61.3 12.8 
4.985 4.806 4.520 4.116 2.549 
41100 46700 51400 53800 61600 
10.624 10.751 10.847 10.893 11.028 
3.56 2.62 1.79 1.14 0.21 
* Volume of the measuring cell is 0.6ml.
3.4 Relationship between P and C
The data of metabolic power (P) and cell concentration (C) in Table 1 and Table 2 indicate that P and C are linearly related (shown in Fig.3). So, we can obtain the corresponding linear equations.
For log phase ,
P = 91.4221 + 0.006561 C ,
with correlation coefficient R = 0.9939 (shown in Fig.3 A). For the decline phase,
P = 429.7061 – 0.006733 C ,
with correlation coefficient R = – 0.9906 (shown in Fig.3 B). Particularly, it can be seen that the P vs. C relationship can be expressed by the common equation
P = A + K C .
Fig.3 Linear relationship of P vs. C
( A: log phase; B: decline phase )
3.5 Relationship between P_{0} and C
The values of heat power output by a single cell, P_{0}, are shown in Table 1 and Table 2. The P_{0} and lnC data taken from Table 1 and Table 2 can also fit linear equations. For log phase,
P_{0} = 34.5026 + 3.6734 lnC,
with correlation coefficient R = 0.9927 (shown in Fig.4 A). For the decline phase,
P_{0} = 93.9499 – 8.5039 lnC ,
with correlation coefficient R = – 0.9962 (shown in Fig.4 B). Particularly, that the P_{0} vs. lnC relationship can be described by the equation
P_{0} = A’ + K’ lnC .
This result indicates that power out by a single cell (P_{0}) depends on the cell population density. In the lag growth phase, the value of P_{0} increased with the increasing of cell concentration (C), it indicates a kind of synergistic action. But, in the decline phase, the metabolism of cell inhibited by metabolites, the value of P_{0} decreased with the increasing of cell concentration (C).
Fig.4 Linear relationship of P_{0} vs. lnC
( A: log phase; B: decline phase )
3.6 Thermochemical equations of metabolism
The P–C data for the growth metabolism were obtained from the thermogenic curve in Figure 2. As described above, P and C are linearly proportional (see Figure 3). P and C relationship is written as:
P = A + K C .
Using the P0 and lnC values from Tables 1 and 2 to fit a linear equation (see Figure 4), the relationship between P0 and lnC should be
P0 = A’ +K’ lnC.
Hence, we can obtain
dC / dP0= K’ C^{n} , n = 1.
with the order of metabolism n = 1 . So, the thermochemical equations of growth metabolism was obtained.
3.7 The mean heat power output of each cell
From the P_{0} data in Table 1 and Table 2, we can calculate the mean heat power output of each cell at different phase. In the log phase, P_{0} is 2.32±1.06 nW.cell^{1}. P_{0} is 1.86±1.16 nW.cell^{1} in the decline phase. These values are close to the value in reference [15].

CONCLUSION
The growth metabolism of Tetrahymena pyriformis cells has been determined. The experimental results indicate that the relationship between cell concentration and heat output can be characterized by the equations,
P = A + K C , P_{0} = A’ + K’ lnC
or P = A + K C, dC / dP0 = K’ C^{n}
for Tetrahymena pyriformis growth metabolism n = 1.
The growth thermokinetic equation is
P_{t} = P_{t=0} exp( k_{m} t) or d P / d t = k_{m} P^{1}
with the order of growth n = 1.
In all of these equations, k_{m}, n, K, A, K’ and A’ are constants for metabolism. These equations are characteristic equations for the growth metabolism of Tetrahymena pyriformis . These equations indicate that the metabolic power linearly correlated to the cell concentration, and that P_{0} (the single cell metabolic power output) depends on the cell concentration.
The experimental results confirmed the applicability of the equations, with good linear correlationship. In general, the growth metabolism of Tetrahymena pyriformis cells can be described by these equations. These equations specifically characterized the growth metabolic process of the Tetrahymena pyriformis and provided a functional relationship for the growth metabolism of environmental protozoa. All of these results are significant of environmental sciences.
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